1
This note contains exams in
TPG4220 DRILLING FLUID HYDRAULICS
Exam 2005
Exam 2006
Exam 2007
Exam 2008
Exam 2009
Exam 2010
Exam 2011
Exam 2012
Exam 2013
and
Solutions to all the exams
All exams tasks are always evaluated for transfer to exercise section. Many of the exam questions have already
been transferred to Exercises in Drilling Fluid Engineering. Relatively few remaining complimentary exams
questions are found here. Some tasks that are too similar to the exercises have also been erased from the exam
pamphlet.
Normally all necessary info, found in the Drilling Engineering Book, is accompanying the exams, but not
presented in this pamphlet.
The following exam-front page is the same every year and not shown for the other exams. The same goes
for additional information:
NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY
DEPARTMENT OF PETROLEUM ENGINEERING
AND APPLIED GEOPHYSICS
Contact person during exam:
Name: Pål Skalle
Tel.: 94925 (secretary), or 91897303 (mobile)
Date for censorship: (latest 3 weeks after exam date)
EXAM IN COURSE TPG4220 DRILLING FLUID
EKSAMEN I EMNE TPG4220 BORESLAM
Tuesday, June 7th, 2000
Tirsdag 7. juni 2000
Time/Tid: 0900 - 1300
Examination support: D: No written or handwritten examination support materials are permitted. Certain,
specified calculator are permitted.
2
Exam TPG4220, 2005
Question 1

Given the Fann VG readings (θ) for different RPMs below, a) Why are these measurements
performed on a continuous base (i.e. every 15 minutes) on the rig? b) Show how to best prepare
the data for pressure loss estimation.
600
60
300
50
200
40
100
30
6
15
3
11
Question 2
The velocity profile is given by vz(r) = umax (l-r2/R2). Compute the pressure distribution dp/dz and the
shear-stress distribution τ in the pipe, on basis of the cylindrical Navier-Stokes equations in the zdirection (horizontal), for fully developed, stationary laminar-pipe-flow where vθ = vr = 0. Find
maximum shear stress in the pipe.
Exam TPG4220, 2006 (no questions left for here)
Exam TPG4220, 2007
1. Clay behaviour
a) When drilling into swelling clay, problems like sloughing (soft) shale and stuck pipe may occur.
Explain how/why this can be avoided by means of the proper oil based drilling fluid and specify
the ingredients in the drilling fluid.
b) Why is KOH preferred over NaOH?
c) What significance does the K+ concentration have for the shale?
2. Pressure loss
Make a graph of pressure loss vs. flow rate in a 1000 m long pipe with inner diameter of 10 cm.
Rheological data points are given below, and mud density is 1.1 kg/l.
Shear rate (s-1)
1022
511
340
170
10
5
Shear stress (Pa)
55
30
20
10
2
1
3
Exam TPG4220, 2008
b)
To control/increase the density of the mud, barite is used. Explain the cause and the negative
effects barite might have during drilling of inclined wells.
c)
Figure out which level and state which the forces are involved in cutting transportation in high
deviation wellbore.
d)
What are the dominating mechanisms or factors leading to mechanically stuck pipe
(differentially stuck not included).
e)
What is the most likely stuck pipe mechanism in salt formations? In case of halite type salts are
present, what kind of mud do you want to use for safe drilling in this salt section.
f)
Makes a note on wellbore breathing (ballooning).
Exam TPG4220, 2009
Task 1
5) Explain what negative effects barite might have during drilling of inclined wells.
9) Properties of mud may be contaminated by salt (NaCl), anhydrite (CaSO4) and cement. Discuss.
Task 4
Mention 5 effects which poor solids control may have on the drilling process.
Exam TPG4220, 2010
4.
Hydraulic program
The bit has 3 · 15/32nd inch nozzles diameter, and ρmud = 1.3 kg/l while drilling at 2500 mMD. The
following pump pressures/rates (which are close to operating flow rates) are recorded;
Test #
1
2
qpump (lpm)
1000
2000
pp (bar)
43
160
a. Determine the value of K1 and m.
b. What is the purpose behind of performing these tests?
5. ECD
If the cuttings concentration generated at the bottom during drilling is 0.02, what will be the
concentration?
1. At the end of the horizontal section
2. At the surface (before leaving the annulus)
4
6. Stability
a. Explain the principal function of the two different surface active additives that are always
added to Oil based mud.
b. How is the salt concentration in the water phase, which is added to Oil Based Mud,
determined?
Exam TPG4220, 2011
1. Pressure loss
a. Show that wall shear stress can be expressed as
for laminar, annular pipe flow, and
b. The cling factor is used during estimation of surge & swab pressure. How would you stepwise
go about to estimate the cling factor?
c. Find the velocity profile in question b for laminar flow with closed-end drill pipe.
Leave out or do only parts of the question if you are in doubt)
2. Solids transportation
a. Are there any countermeasures to barite sagging?
b. What determines cuttings bed height?
c. Why is cuttings accumulation in wellbore expansions (washouts) a problem?
3. Bit hydraulics
How do you determine when to change from working area I to II of the pump during drilling?
5. Wellbore stability
The drilling fluid water’s phase has an identical water activity with pore water. The water will
penetrates shale in accordance with Darcy’s law, although in small quantities. Is it possible for a mud
engineer to reduce this flow of water (a reduction is beneficial because it will reduce unwanted
reaction between the drilling fluid water phase and shale further away from the wall, where the pore
water activity is different)?
Exam TPG4220, 2012
Task 2. Pressure loss
A drilling fluid has been tested with this result.
RPM
600
300
100
3
Reading
140
98
54
13
= Reading x 1.06 x 0.4788
= RPM x 1.703
5
a.
b.
c.
Find Bingham and Power Law constants, for Bingham both through Field procedure and ordinary
straight line constants.
Find pressure loss in a 10 m long 6 ¾” x 12 ¼ “ annulus when pumping at 400 lpm. Use Power
Law. Ρmud = 1100 kg/m3.
What effect has entrance length of a uniform pipe on estimated pressure loss?
Task 4. Solids control
Explain why the height of the solids bed in a wellbore was 2.5 inches.
Task 5. Hydraulic program
Describe how you make a computer program to select the optimal flow rate and the optimal nozzle
size for one wellbore section (all liners are treated as being in Range I). Assume the boundary
conditions are as here:
qmax 5”
qr
qmax 6”
qmax.well
qmax 7”
Give a short explanation to the flow chart you make, so that others also understand it.
Exam TPG4220 2013
1. Mud hydraulics
In this task you are asked to:
a. Verify the shear rate expression for a Bingham fluid (see Appendix), both for pipe and annular
flow. To find the answer you need to derive the so called universal pressure loss model.
b. Prove that the pump pressure is generated purely by friction resistance in the flow system (use
a control volume in the fluid circulating system to prove it).
2. Swab during tripping out
Assume you are tripping out while simultaneously pumping. Your task is to start the process of
derivation, which later (not in the exam), will lead to an expression of surge pressure during laminar
flow. When making a drawing, use parameters like vp (pipe), qp (pump), Rw (wellbore), Rp (pipe), R0
(the point where the flow velocity is zero), etc, as required for your explanation.
3. Hydraulic program
Pump characteristics of a 1600 Hp pump are given in the Appendix. While drilling in the 12 ¼ “ well
section at 3 000 mMD, the hydraulic constants are determined:
m = 1.7 (-)
K1 = 2.0 . 106
qr = 0.03
mud = 1 300
(kg/m4)
(m3 / s)
(kg/m3)
a. Show that pbit = pp . m / (m+2)
b. Determine the optimal hydraulic parameters while drilling at 3 000 and at the end depth of 4
500 mMD. Assume the hydraulic constants remain unchanged in this interval.
c. Sketch an artistic log-log plot (standard graphic solution technique) of the situation at 3 000
and at 4 500 m (in the same plot).
6
4. Wellbore stability
While drilling in the 8 ½ “ section, at a depth of 1 500 mTVD / 6 000 mMD, in overbalance, the ECD
will fluctuate and at times be high in this long well. Previous experience from that area indicates that
instable, swellable shale will be penetrated. Your task now is the following:
a. Define what wellbore stability-related processes may take place in the shale while drilling
through it with WBM.
b. Which type of inhibitive mud will you suggest in order to maximize wellbore stability?
Explain how this mud type will affect the wellbore.
c. Does fluctuating ECD have any implications for the stability of the wellbore?
7
Solution Exam TPG4220, 2005
Question 1
 a) To monitor if any contaminants are encountered
b) Best preparation is to find the rheology model that fits best. This must be performed through a
regression test and select the one with the highest R2 or compare manually To compare manually
we need to compute the parameters in the different models (Power law and Bingham) and plot the
results and compare with real data.
= 6 – 50 = 10 cP = 0.01 Pas
= 300 – pl = 40 lb/100 ft2 = 19.2 Pa
= 0.26
µpl
τo
n
Question 2
Navier stoke in z-direction, cylindrical coordinates
z
 1   v z  1  2 v z  2 v z 
 z
1 p

 
 2 
r
 2
2
z
 z
z 
 r r  r  r 
For given flow it reduces to
0
1 p
 z

1   v z 
r

r r  r 
Rearranged
p
1   v z 

r

z
r r  r 
From flow profile we obtain
v z
 2r 
 um   2 
r
 R 
Last part of the equation (1):  r  u m   2r2    u m  2 2r
2
r

R 
R
Pressure distribution or pressure gradient becomes:
p
1  u  4r 
    m 2 
z
r
R 
Total pressure loss along z:
z
z
o
o
 p   
4 u m
z
R2
p  4u m z / R 2
The shear stress is found as    
v
   u m  2r / R 2 .
r
Maximum of  is found when r = R, i.e. at the wall.
 max  2  u m / R
Solution Exam TPG4220, 2007
1. Clay behavior
a)
By adding salt to the mud’s water phase corresponding to Aw of pore water. No osmotic force
between mud and clay, and thus no water driven swelling. There are 5 ingredients in OBM, the
Aw and the salt type should be as close to pore water’s as possible.
8
1.
2.
3.
4.
5.
Base oil
Water
Emulsifier (surface active additive I)
Surface wetting (surface active additive II)
Salt
c)
K+ is geometrically suitable in between platelets and leads to high platelet attraction (low
swelling).
d)
The higher concentration, the more Na++ is exchanged.
2.
a)
Flow in pipes
p
 1 
rv 
 
z
 r r r

From boundary condition, rearranging/integrating twice v (r ) is found. Or simply starting by
From attachment and stated condition; 0  
equating shear forces with pressure forces on a small element.
b)
w   
c)
v
dv
dp / dx
R dp

  2 R   
dr
4
2 dx
R

(shear stress is highest for r = R)

1
1 dp / dx
R 2 dp / dx
2
2
(dA = π 2 r dr)
v
dA

R

r
2

r
dr


A
8

R 2 4 o
The two eqn. above are valid only for laminar flow.
d)
dp/dx = 0,09 MPa/1000 m = 90 Pa/m
w  
0.05
90  2.25 Pas
2
3. Pressure loss
Clearly a Newtonian fluid  
v  q/A,
N Re 
v
0.05 2
90

 0.53 m s
8
0.0538

55

 0.0538 Pas 54 cP 
 1022
 vdh

Select two in laminar and two in turbulent regime
l/m
250
500
1000
2000
Pressure
q
m3/s
0.00417
0.00833
0.017
0.033
v
m/s
0.53
1.06
2.12
4.25
NRe
1083
2170
4340
8687
p
MPa
0.09
0.18
0.85
2.98
Turbulent pressure loss model
Laminar pressure loss model
Flow Rate
9
Solution Exam TPG4220, 2008
1: Short questions
b.
Cause of Barite segregation
 Barite has a specific density of 4.3, average particle size of approximately 20 microns and will
thus stay in suspension for long periods of time in a viscous fluid, but slip slowly due to
gravity.
 When mud density is greater than 1.5 kg/l the
concentration is so high that barite tends to
agglomerate and sediment at higher rates.
 Sagging takes place only at inclinations between
30-60 deg.
Negative effects of sag
 It causes hole plugging /surge pressure / lost
circulation
 It causes Stuck pipe
c.
High ROP, high inclination, highly viscous mud,
rolling, lifting etc.
g. Problem:
-
stuck pipe, salt creep
drill string wash out,
cracks,twist offs and
Casing collapse loading.
WBM can be used with some additives. Halite has little creep tendency.
h. Wellbore breathing (ballooning)




The onset of wellbore breathing, often referred to as wellbore ballooning, is typically an
indicator of imminent lost circulation.
Wellbore breathing is associated with fractures that open when annular pressure is applied to
the Wellbore and close when pressure is reduced.
These fractures will be filled with drilling fluid when open and subsequently return the fluid,
observed as a flow out of the wellbore, when the pumps are turned off.
One of the more severe consequences of wellbore breathing is the misinterpretation of the
observed flow as a kick when the pumps are shut down.
Solution Exam TPG4220, 2009
Task 1
Salt:
-Addition of thinners to reduce viscosity
-Addition of caustic soda to increase pH
Anhydrite: Addition of sodium carbonate to remove the excess calcium ions:
Na2CO3 + CaSO4 = CaCO3 + Na2SO4
(CaCO3 is precipitated as an insoluble material)
10
Cement: Addition of sodium bicarbonate to remove the excess calcium ions:
NaHCO3 + Ca(OH)2 = CaCO3 + NaOH + H2O
(CaCO3 is precipitated as an insoluble material)
Task 4
Some effects on the drilling process, related to poor solids control are:
mechanical stuck pipe
higher mechanical friction / reduction in ROP
thicker mud cake / differential sticking
denser mud, high pressure losses / ECD
difficulties during tripping of drill string and casing.
Solution Exam TPG4220, 2010
4a.
p pump  ploss  pbit
1000 
15



vnozzle1  q / 3  d 2  
/  3   / 4   0.0254 
32
 4  1000  60 

pbit1  18 bar ,  bit 2  72 bar
ploss1  43  18  25 bar
ploss2  160  72  88 bar
m = log ( 88 ) / log  2 / 1  = 1.86 K 1 = ca 2.0 · 10 6
25
 60
60 
Find p d  p p  pbit
1
p bit 1.11 v 2
2
v = q/Anozzle
Abit
= (π/4)de2
= π/4 (d12 + d22 + d32) = π/4 ∙3 ∙ (15/32)2 ∙ (2.54*10-2)2 = 3.3333 ∙10-4 m2
q1 = 0.03333 m3/s,
q2 = 0.017 m3/s,
v1 = 100 m/s,
v2 = 51 m/s
d e  d1  d 2  d 3  3  d1  3 
2
q (lpm)
2000
1000
2
2
pp (bar)
160
43
15
0.0254  0.0206 m
32
∆pbit
72
18
∆pd
88
25
K1D and m are determined from: pd  K1D q m
m
ln p d 1 pd 2 
ln 88 25

 1.82
ln q1 q2 
ln 2000 1000
K1 D  p d q m 
88  105
6
 43  108 /2500 = 1.7 * 10 = K1
1.82
0.0333
1
11
4b.
1. To find  loss for “normal” operating conditions
2. To find optimal flow rate and nozzles size to obtain optimal ROP.
5a.
Settling and lifting of cuttings is a function of q, rpm, A flow etc. in average or at an
equilibrium cuttings height Ch is slightly lower than Co since some cuttings are always
deposited, e.g. Ch = 0,95 · C.
5b.
Csurface = Ch / Rtransport , typically twice as high as the original concentration.
6a.
Emulsifier is used to reduce the surface tension between oil and water, enabling smaller
droplets, enhancing stability. Wetting agents make sure that oil is wetting the shale.
6b.
Find the Aw of clay through its in situ weight and then by comparing with clays with known
Aw. Thus Aw of water phase is determined, and type of salt.
Solution Exam TPG4220, 2011
2. Pressure loss
a.
Force Balance:
→
And solving ΔpNewton = ΔpBingham for µeff gives the answer.
b.
1. Make a detailed drawing where all parameters are defined
2. Develop velocity profile with the correct boundary condition
3. Mass balance: qup = vpipe ·vpipe + qcling. (mass-up = mass-down)
4. Cling factor: qcling/qdown
3. Solids transportation
b.
1. Making the solids particles smaller or even replace them by high density salt.
2. Tripping faster.
3. Increase viscosity just before tripping.
4. Down hole flow enhanced mounted on the drill string.
c. The cuttings removal forces are countered by gravity and cohesive forces. Gravitational forces are
given by Stokes law. Cohesive forces are influenced by the mud’s gel strength. Removal forces
given by drag and lift forces. Drag forces are a function of particle Reynolds number and
spherisity. These forces can be developed into the critical lift velocity or rolling velocity. At a
given cuttings feed rate, a stationary bed height will form as a function of all involved input
variables. Rotation will enhance removal.
d. Here the bed height will be higher due to higher cross sectional area and thus lower Reynolds
number. When BHA is shoveling many cuttings into a narrower wellbore it is easy to imagine that
the BHA may become jammed.
4. When to shift
You start in area II and drill until the depth where qopt II = qmax,smalles liner. Then you turn to qmax,smallest liner
and turn to qopt I at the depth when qopt I = qmax,smallest liner
5. Wellbore stability
a. Yes, it can be reduced by creating a filter in the shale. This can be done by adding particles to
the water phase where the average particle size distribution 1/3 of the average pore throat
size distribution.
12
Solution Exam TPG4220, 2012
2. P-loss
a.  pl   600   300  140  98  42 cP
YP   300   pl  98  42  56 lb / 100 ft 2  28.4 Pa
 pl 
140  98 0.4788 1.06  41.710 3 Pas
600  300 1.703
YP   2   pl   2  71.06  41.07  10 3  1022  28.4 Pa
n  log  2 /  1  / log  2 /  1   0.51, K  2.08 Pas  n
b.
1. Check NRe = ρvd/µeff  Find µeff
2. Find Δploss
v = q/A = 0.435 m/s.
n
 eff
N Re
 12v 2n  1  K  d
 
 

 0.4 Pas
3n  12v
 dn
vd

 200
 eff
n
 12v 2n  1  L
 
p a  4 K 

 0.04 10 5 Pa
d
3
n
d
h
 h

c.
A uniform pipe has an entrance length. Increasing length with increasing NRe
Undeveloped flow at the entrance is turbulent and has higher shear until boundary layer
expands and meets in the middle.
4. Solids control
Bed height can be described with 26 words:
Drag Force (shear stress, viscosity, spherisity, Reynolds N,)
Gravitation (particle diameter, , concentration, transp. ratio)
Cohesive F (YP, van der Waal)
Critical v (friction factor, pump rate, bed height)
Mechanical F (rotation, reciprocation, reaming)
Hole geometry ( dhydr, washouts, inclination)
5. Hydr.progr.
1. Find which liner:  assume smallest possible liner in the vertical section. In the horizontal section
there might be other optimal criteria than for vertical wells (max ROP).
2. Find depth where changes of liner, qmax, qr, etc is occurring.
3. Find dnozzle from Δpbit = Δpbit,optimal
a. Define as precisely as possible in terms of flow rate q, or velocities v, the fluid pattern during
the steady-state upward pipe movement (tripping out). Draw two sketches, one without
simultaneous pumping and one including pumping.
b. Explain how you will determine the swab pressure, just in principle terms, preferably
stepwise.
13
Solution exam TPG4220 2013
1. a.
Bingham:
b. From the Bernoulli’s equation we see that all parameters are identical in and out of a control
volume of a horizontal (or vertical) pipe, except for the friction term. Can also be proved
through pointing at pressure forces= shear forces in laminar pipe flow.
2. a. The Vcling will be added to the fluid volume displaced by the drill string.
qDS = ADS · vDS, vdisplaced = qDS/Aflow
Vtotal = Vpump – Vdisplaced - Vcling
b. Step 1. Understand the physics and forces in a Drawing
Step 2. Make a control box and entering exiting forces.
Δp·πr2 = τ·2πrΔL
Δp/ ΔL ·r = 2τ
Step 3. Differentiate: Δp/ ΔL ·dr = 2 dτ
Step 4. Integrate over the control volume (along r)
3. a.
pb = Δpd + Δpbit
= 2pp ·q – (m+2) K1Dqm+1 = 0
= 2pp – (m+2) K1Dqm
=0
= 2pp – (m+2)(pp – Δpbit) = 0
→ Δpbit =
Alternatively: qopt = 2pp/[(m+2)K1D]1/m
 K1Dqoptm = pd = 2pp/(m+2)
b. From pump characteristics we see that, to optimize available pressure, in a vertical well, liner 5
¾” must be chosen; pmax = 350.6 bar. In a horizontal well one have to start with a flow rate
higher than qr.
= 1.11 . ½ . v2
c.
4. a. Water flow, ion-flux, pressure flux, due to …….
b. Osmotic, non-invading drilling fluid, as shown in figure …..
c. Cyclic spalling, but also fractures and kick